Bump Microsoft.Private.Intellisense to 20241010.1

[carlossanlop]

Updating to consume the nuget package with the last batch of docs from dotnet-api-docs for RC2. https://dnceng.visualstudio.com/public/_artifacts/feed/dotnet9-transport/NuGet/Microsoft.Private.Intellisense/overview/9.0.0-preview-20241010.1

Already updated source build dotnet/source-build-reference-packages#1055

Need to backport to release/9.0 (also updated source build in that branch: dotnet/source-build-reference-packages#1056)

[carlossanlop]

/backport to release/9.0

[github-actions]

Started backporting to release/9.0: https://github.com/dotnet/runtime/actions/runs/11281517900

[dotnet-policy-service]

Tagging subscribers to this area: @dotnet/area-infrastructure-libraries
See info in area-owners.md if you want to be subscribed.

[github-actions]

@carlossanlop backporting to release/9.0 failed, the patch most likely resulted in conflicts:

$ git am --3way --empty=keep --ignore-whitespace --keep-non-patch changes.patch

Applying: Bump Microsoft.Private.Intellisense to 20241010.1
Using index info to reconstruct a base tree...
M	eng/Versions.props
Falling back to patching base and 3-way merge...
Auto-merging eng/Versions.props
CONFLICT (content): Merge conflict in eng/Versions.props
error: Failed to merge in the changes.
hint: Use 'git am --show-current-patch=diff' to see the failed patch
hint: When you have resolved this problem, run "git am --continue".
hint: If you prefer to skip this patch, run "git am --skip" instead.
hint: To restore the original branch and stop patching, run "git am --abort".
hint: Disable this message with "git config advice.mergeConflict false"
Patch failed at 0001 Bump Microsoft.Private.Intellisense to 20241010.1
Error: The process '/usr/bin/git' failed with exit code 128

Please backport manually!

[github-actions]

@carlossanlop an error occurred while backporting to release/9.0, please check the run log for details!

Error: git am failed, most likely due to a merge conflict.

[carlossanlop]

Blocked by dotnet/source-build-reference-packages#1055 as it needs to flow to runtime first.

[carlossanlop]

/azp run runtime-dev-innerloop

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[carlossanlop]

@dotnet/runtime-infrastructure @dotnet/area-infrastructure-libraries can I get a sign-off?